class window : public window_base
{
private:
    std::function<void(renderer::*)()> m_display_callback_;
...
    void window::set_render_callback(renderer* rndr)
    {
        m_display_callback_ = [=]()->void{ rndr->clear(); rndr->display(); };
    }
}

void f(){}

std::function<void()> m_display_callback_;

m_display_callback_ = аж

static void f(renderer* rndr) { rndr->clear(); rndr->display(); }

void set_render_callback(renderer* rndr)
{
    //m_display_callback_ = [=]()->void{ rndr->clear(); rndr->display(); };
    m_display_callback_ = std::bind(f, rndr);
}